In Computation, Parallel is Nothing, Physical Everything

Abstract

Andrew Boucher (1997) argues that ``parallel computation is fundamentally different from sequential computation'' (p. 543), and that this fact provides reason to be skeptical about whether AI can produce a genuinely intelligent machine. But parallelism, as I prove herein, is irrelevant. What Boucher has inadvertently glimpsed is one small part of a mathematical tapestry portraying the simple but undeniable fact that physical computation can be fundamentally different from ordinary, ``textbook'' computation (whether parallel or sequential). This tapestry does indeed immediately imply that human cognition may be uncomputable.